Lipschitz-free spaces and Bossard's reduction argument

2025/08/31 by Smith, Richard J.
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2509.00722

Abstract

Motivated by recent work of E. Basset, G. Lancien and A. Procházka, we use the reduction argument of Bossard to prove two results: if a separable Banach space is isomorphically universal for the class of Lipschitz-free spaces over the countable complete discrete metric spaces then it is isomorphically universal for the class of separable Banach spaces, and if a complete separable metric space is Lipschitz universal for the same class of metric spaces then it is Lipschitz universal for all separable metric spaces.

Citations

• Diversity of Lipschitz-free spaces over countable complete discrete metric spaces
• Lipschitz-free spaces over strongly countable-dimensional spaces and approximation properties
• On the weak-fragmentability index of some Lipschitz-free spaces
• Lipschitz-free spaces over properly metrisable spaces and approximation properties
• Lipschitz-free spaces over Cantor sets and approximation properties
• Lipschitz-Free Spaces over Manifolds and the Metric Approximation Property
• Extremal structure and Duality of Lipschitz free spaces
• Approximation and Schur properties for Lipschitz free spaces over\n compact metric spaces
• Products of Lipschitz-free spaces and applications

Related

• Products of Lipschitz-free spaces and applications
• Diversity of Lipschitz-free spaces over countable complete discrete metric spaces
• A complete metric space without non-trivial separable Lipschitz retracts
• A note on nonseparable Lipschitz-free spaces
• Coarse and Lipschitz universality